Pub Date : 2024-02-15DOI: 10.1088/1361-6404/ad2391
Colin S Wallace, Liam Jones, Alex Lin
In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the r (or r2) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.
{"title":"Four errors students make with inverse-square law vectors","authors":"Colin S Wallace, Liam Jones, Alex Lin","doi":"10.1088/1361-6404/ad2391","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2391","url":null,"abstract":"In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the <italic toggle=\"yes\">r</italic> (or <italic toggle=\"yes\">r</italic>\u0000<sup>2</sup>) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1088/1361-6404/ad2392
Thales Azevedo
When studying (or teaching) classical electromagnetism, one is bound to deal with the electric field of an ideal electric dipole, as well as its magnetic counterpart. A careful analysis then reveals that each of those fields must include, for consistency, a term proportional to a Dirac delta function localized at the position of the dipole. However, one is usually told not to worry about those terms since, as classical interactions always involve sources which are spatially separated, the Dirac-delta terms are only relevant for quantum mechanics, where they are directly related to important phenomena. In this work, we pose and solve a purely classical problem in electrostatics in which the Dirac-delta terms in the dipole fields are indispensable. It involves the computation of the interaction energy between a conductor with a spherical cavity and an (ideal) electric dipole located at the center of that cavity. We also solve its magnetic counterpart, replacing the conductor with a superconductor and the electric dipole with a magnetic one.
{"title":"Can the Dirac deltas in dipole fields be ignored in classical interactions?","authors":"Thales Azevedo","doi":"10.1088/1361-6404/ad2392","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2392","url":null,"abstract":"When studying (or teaching) classical electromagnetism, one is bound to deal with the electric field of an ideal electric dipole, as well as its magnetic counterpart. A careful analysis then reveals that each of those fields must include, for consistency, a term proportional to a Dirac delta function localized at the position of the dipole. However, one is usually told not to worry about those terms since, as classical interactions always involve sources which are spatially separated, the Dirac-delta terms are only relevant for quantum mechanics, where they are directly related to important phenomena. In this work, we pose and solve a purely classical problem in electrostatics in which the Dirac-delta terms in the dipole fields are indispensable. It involves the computation of the interaction energy between a conductor with a spherical cavity and an (ideal) electric dipole located at the center of that cavity. We also solve its magnetic counterpart, replacing the conductor with a superconductor and the electric dipole with a magnetic one.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-12DOI: 10.1088/1361-6404/ad2101
Joaquim Anacleto
We present the fundamental equation for a system and for a process, and by considering irreversibility within the system, we show that the lost work concept emerges naturally from the formalism. We then argue that if irreversibility is considered within the surroundings the lost work becomes what is known as exergy. Therefore, lost work and exergy are two views of the same concept, which in turn integrates a broader and more fundamental concept: entropy generation. It is our opinion that the clarification of the meanings of lost work and exergy, as well as the discussion that leads to an understanding of their differences and similarities, has not received the attention in the literature that it deserves. This paper fills that gap, and it is hoped that the discussion of these two concepts here will be useful for both students and teachers.
{"title":"Lost work and exergy: two views of the same concept","authors":"Joaquim Anacleto","doi":"10.1088/1361-6404/ad2101","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2101","url":null,"abstract":"We present the fundamental equation for a system and for a process, and by considering irreversibility within the system, we show that the <italic toggle=\"yes\">lost work</italic> concept emerges naturally from the formalism. We then argue that if irreversibility is considered within the surroundings the lost work becomes what is known as <italic toggle=\"yes\">exergy</italic>. Therefore, lost work and exergy are two views of the same concept, which in turn integrates a broader and more fundamental concept: <italic toggle=\"yes\">entropy generation</italic>. It is our opinion that the clarification of the meanings of lost work and exergy, as well as the discussion that leads to an understanding of their differences and similarities, has not received the attention in the literature that it deserves. This paper fills that gap, and it is hoped that the discussion of these two concepts here will be useful for both students and teachers.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-16DOI: 10.1088/1361-6404/ad1531
Zeynep Tugce Ozkarsligil, Bayram Tekin
We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency f1, the maximum detected frequency (chirp frequency) f2, and the time elapse τ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.
{"title":"Mass formulas for individual black holes in merging binaries","authors":"Zeynep Tugce Ozkarsligil, Bayram Tekin","doi":"10.1088/1361-6404/ad1531","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1531","url":null,"abstract":"We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency <italic toggle=\"yes\">f</italic>\u0000<sub>1</sub>, the maximum detected frequency (chirp frequency) <italic toggle=\"yes\">f</italic>\u0000<sub>2</sub>, and the time elapse <italic toggle=\"yes\">τ</italic> between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-29DOI: 10.1088/1361-6404/ad1398
Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov
We consider in detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.
{"title":"Berry phase of spin-one system in a rotating electric field","authors":"Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov","doi":"10.1088/1361-6404/ad1398","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1398","url":null,"abstract":"We consider in detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-29DOI: 10.1088/1361-6404/ad139a
Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler
The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing Up of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.
布洛赫球表示法是两级系统所有可能量子态的几何模型，可用来描述量子比特的时间动力学。作为明确的应用，我们考虑了双阱势中粒子的时间动力学。特别是，我们采用了一种最新的非共振激发方法，即在周期性电磁场驱动下的所谓 SUPER 原理（量子发射器群的摆动上升），将其应用于量子隧穿。我们的研究表明，当引入适当的势高振荡时，隧穿概率会显著提高。在我们称之为 "教育者-开发者对话 "的合作方法的推动下，我们推出了软件 Quantum Composer 的更新版本。出于教育目的，我们将一维薛定谔方程的两个最低能量状态映射到布洛赫球表示法中，从而为相关的时间动力学提供了一幅相当清晰直观的物理图景。
{"title":"Modelling assisted tunneling on the Bloch sphere using the Quantum Composer","authors":"Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler","doi":"10.1088/1361-6404/ad139a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad139a","url":null,"abstract":"The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing Up of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call <italic toggle=\"yes\">educator-developer dialogue</italic>, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reply to Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Palash B Pal","doi":"10.1088/1361-6404/ad0dea","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0dea","url":null,"abstract":"This note contains my response to the comment written by J Franklin on my paper ‘Covariant formulation of electrodynamics in isotropic media’.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"205 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139054611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-15DOI: 10.1088/1361-6404/ad0f9b
P-M Binder
The predominantly Greek and Latin etymological roots that form the core introductory physics vocabulary are identified. They number slightly over 260. Words with other origins and common suffixes are also listed. Definitions are also given for a group of words that have caused difficulties for students in physics classes, contrasting meanings that are, and are not related to physics. A reverse dictionary of roots, showing the individual origin of about 400 words in all areas of introductory physics is presented in an appendix. The information presented here can inform and assist in developing a physics lexicon in minority and indigenous languages and to create classroom moments that connect the origin of words with everyday life.
{"title":"The origins of physics words","authors":"P-M Binder","doi":"10.1088/1361-6404/ad0f9b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0f9b","url":null,"abstract":"The predominantly Greek and Latin etymological roots that form the core introductory physics vocabulary are identified. They number slightly over 260. Words with other origins and common suffixes are also listed. Definitions are also given for a group of words that have caused difficulties for students in physics classes, contrasting meanings that are, and are not related to physics. A reverse dictionary of roots, showing the individual origin of about 400 words in all areas of introductory physics is presented in an appendix. The information presented here can inform and assist in developing a physics lexicon in minority and indigenous languages and to create classroom moments that connect the origin of words with everyday life.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1088/1361-6404/ad0de9
Jerrold Franklin
A recent paper Pal (2022 Eur. J. Phys.43 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, Fμν, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives Fμν for a medium moving with constant velocity, v, in terms of Fμν for the medium at rest. However, although Fμν has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.
最近的一篇论文 Pal (2022 Eur. J. Phys.43 015204) 以共变形式将相对论经典电磁学从自由空间扩展到线性可极化介质。论文基于这样一个假设：相对论张量 Fμν 在自由空间中是一个张量，在线性介质中也是一个张量。Pal 提出了一种协变公式，用静止介质的 Fμν 来表示以恒定速度 v 运动的介质的 Fμν。然而，尽管 Fμν 已被证明是自由空间中的相对论张量，但我们证明它在线性介质中并不是张量。这意味着帕尔提出的协变扩展失败了。
{"title":"Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Jerrold Franklin","doi":"10.1088/1361-6404/ad0de9","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0de9","url":null,"abstract":"A recent paper Pal (2022 <italic toggle=\"yes\">Eur. J. Phys.</italic>\u0000<bold>43</bold> 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup>, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives <inline-formula>\u0000<tex-math>\u0000<?CDATA ${F}^{mu nu }$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ejpad0de9ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> for a medium moving with constant velocity, <bold>v</bold>, in terms of <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> for the medium at rest. However, although <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1088/1361-6404/ad1530
K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer
A method to derive the Fraunhofer diffraction integral by making use of the theory of distributions is presented. With respect to standard textbooks, the pedagogical benefit of this method is that it uniquely uses the far field approximation of the Fresnel diffraction integral. An operator representation of Fresnel diffraction is also derived.
{"title":"Fraunhofer approximation of Fresnel integrals","authors":"K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer","doi":"10.1088/1361-6404/ad1530","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1530","url":null,"abstract":"\u0000 A method to derive the Fraunhofer diffraction integral by making use of the theory of distributions is presented. With respect to standard textbooks, the pedagogical benefit of this method is that it uniquely uses the far field approximation of the Fresnel diffraction integral. An operator representation of Fresnel diffraction is also derived.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"105 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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